I've found Japanese greens like "softer" water than oolongs or other types of tea. I sometimes adjust what I'm drinking according to where my filter is at in terms of it's lifespan.

I will sometimes wait to start a really premo puerh or roasted oolong until the end of the cartridge life, where all of the activated charcoal is washed out and more minerals are getting through. I also have mixed bottled spring water in with the filtered water with good results.

Also, I use water that is relatively recently filtered... if it's been sitting in the pitcher more than a day I tend to drink it or use it to heat the pot and run fresh water through for the actual brewing.

Soft water brings out all the flavors in a tea, both good and bad. So if the tea and the brewing technique are top-notch, this will provide best results, otherwise your results will vary.

Hard water releases flavors selectively from tea. A tea that might taste unpleasant using soft water will probably taste alright using hard water, because many of the unpleasant flavors will remain in the leaves. A delicate tea might taste bland in hard water for the same reason, because many of the pleasant flavors remain in the leaves. Lu Yu, the ancient Chinese tea master, believed that hard water (water from stalactite springs was his term) is the best choice for tea. On the other hand, in his day the treatment of tea was much harsher, and it was trickier to control the brewing variables.